Paris St Germain underlined their status as European champions by beating Barcelona 4-2 in a blockbuster Champions League clash on Tuesday, while Liverpool and Manchester City ​also claimed victories.

Desire Doue, Lucas Hernandez, Vitinha and Fabian Ruiz scored for PSG, with Xavi Espart and Lamine Yamal twice pulling Barcelona level ‌in the second half.

Alexis Mac Allister scored twice as Liverpool fought back from two goals down to beat Villarreal 4-3 in a thrilling encounter at Anfield.

Phil Foden scored a hat-trick to lead Manchester City to a 5-1 win over AEK Athens at the Etihad Stadium, with Elliot Anderson and Rayan Cherki also on the scoresheet as Erling Haaland was rested.

PSG outlast Barcelona

Barcelona arrived at the ​Parc des Princes with a perfect record across all competitions this season, but PSG proved more clinical in a breathless contest to hand the Catalans their first ​defeat of the campaign.

The relentless tempo took its toll, with PSG's Ousmane Dembele, Khvicha Kvaratskhelia and Marquinhos, along with Barcelona's Dani ⁠Olmo, all forced off through injury.

PSG peppered the Barcelona goal in the opening five minutes, with Kvaratskhelia hitting the post, before the game settled into a rhythm.

The ​hosts gradually took control of midfield and went ahead after Yamal surrendered possession in his own half, allowing Doue to drive a fierce low shot into the corner.

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Goalkeeper ​Joan Garcia produced several saves to keep Barcelona in the contest before Espart, making his first Champions League start, created and finished a superb move to equalize in the 55th minute.

Ferran Torres hit the post against his former club before Hernandez headed PSG in front from a corner in the 72nd minute, starting a burst of four goals in 14 minutes.

Lamine equalized again for ​Barcelona with a brilliant individual effort in the 79th minute, before Vitinha responded for PSG with a fine strike 109 seconds later.

As Hansi Flick's side searched for ​an equalizer, Fabian Ruiz converted an Achraf Hakimi cross at the back post to seal the victory.

The result lifted PSG onto nine points and top of the Champions League standings, ahead of Liverpool ‌on goal ⁠difference.

Foden hits three

Foden netted a hat-trick as Man City comfortably dispatched AEK Athens at the Etihad Stadium.

Anderson opened the scoring for the hosts in the 12th minute before Foden doubled the advantage in the 34th.

AEK Athens pulled a goal back through Stavros Pilios in the 52nd minute, but Cherki restored City's two-goal cushion five minutes later.

Foden added his second of the night in the 65th minute and completed his treble 11 minutes later to wrap up a dominant performance.

Haaland was an unused substitute, as City ​gave their leading striker a rest amid ​a demanding fixture schedule.

Liverpool edged Spanish ⁠side Villarreal after a stirring comeback.

The visitors stunned the home crowd when Georges Mikautadze struck in the fourth minute before Sergi Cardona doubled Villarreal's lead in the 29th.

Liverpool's fightback started with two headers as Mac Allister pulled a goal back in the ​36th minute before Ronald Araujo equalized in first-half stoppage time.

Mac Allister completed the turnaround with his second goal in the ​65th minute, and Florian ⁠Wirtz hammered home a fourth in the 69th to cap a rampant spell for the hosts.

Tani Oluwaseyi pulled one back for Villarreal in the 87th minute, but Liverpool survived the late pressure to secure the points.

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Atletico Madrid's Julian Alvarez levelled in the second half to earn them a 1-1 draw with VfB Stuttgart, who took the lead through Jamie ⁠Leweling before the ​break. Morten Hjulmand was sent off in the 64th minute, leaving Atletico with 10 men for ​the closing stages.

Napoli edged Bodo/Glimt 4-3 and PSV Eindhoven held off Porto for a 1-0 win, while AS Roma cruised to a 4-0 victory over Slovan Bratislava.

Earlier, Borussia Dortmund won 2-1 against Champions League debutants ​Sabah, while a 90th-minute equalizer from Pavel Kacor earned Slavia Prague a point in a 2-2 draw at Fenerbahce.